Sept. 5 , 1958
STRUCTURE OF TETRAGONAL BORON
and the reduction (or oxidation) is attributable to the difference between these two rates. The exchangeable surface oxygen, ns,of ZnFe204 is about five times larger than that of ZnCr204 and about thirty times larger than that of ZnAlz04. This relationship is in qualitative agreement with the order of the amounts of l80transferred to carbon monoxide (Table 11): ZnFez04 > ZnCrzOe > ZnA1204. The tendency of the catalysts to be reduced or oxidized coincides with their oxidizing power; ZnFez04 will oxidize this gas more readily than ZnCr204, while ZnAlzOcwill reduce it slightly, as one might predict from its tint. Now let us consider the nature of the surface state of these catalysts. No transfer of lSOto carbon monoxide was observed even a t 300" with grayish green ZnCrzOewhich had been slightly reduced with hydrogen a t 100 mm. for 30 minutes a t 480". Another sample of ZnCrzO~,which had been evacuated a t 10W3mm. a t 500"for 1 hr., also lost its catalytic activity. Neither treatment caused any change which could be observed by Xray diffraction analysis. This suggests that the excess oxygen on the surface of ZnCrz04,a p-type semi-conductor, is essential for its catalytic activity. Hence, for ZnCr204,(K)O in ( 2 ) represents the presence of excess oxygen and (K) its disap[CONTRIBUTION FROM THE
4507
pearance, which is caused by reduction by the ambient gas. ZnAlzO4 and ZnFezO4 are n-type semi-conductors; ZnAlz04prepared in this study was reduced somewhat from the stoichiometric composition. In ZnFe204,and inverse spinel, the iron ions distributed as Fe+++ both in the 8f and 16c positions are liable to exchange the valency as Fe+++ Fe++. Accordingly, (K) and (K)O correspond in ZnAlz04to the defect of surface oxygen and to the state where the defect is filled with oxygen atoms; and in ZnFe204,to the site around a reduced iron ion, and to that around which all the iron ions are oxidized. For the elucidation of the precise nature of (K)O and (K) and the identificaiion of the rate-determining steps, further investigation is necessary. Acknowledgments.-The authors are indebted to Assistant Professor Shun Araki for his help with the isotopic analyses and for making the mass spectrometer available, to Mr. Fujio Mochizuki for practical assistance and Mrs. Weissberger for her elaborate revising of the manuscript. The expense of this research has been in part defrayed by a Grant in Aid from the Ministry of Education. BUNKYO-KU, TOKYO, JAPAN
DEPARTMEST OF
CHEMISTRY, CORSELL UNIVERSITY]
The Structure of Tetragonal Boron] Bu J. L. HOARD, R. E. HUGHESAND D. E. SANDS RECEIVED MARCH 29, 1958 The fifty boron atoms of the tetragonal unit are divided among four approximately regular icosahedra centered in the '(2 0. Each positions '/4 '/4 ' / l , 3/4 3/4 I/* 3/4, ' / 4 a / 4 "4 of Piz/nnm with two individual atoms in 2b:OO l / 2 , boron atom of an icosahedron forms six bonds directed toward the corners of a pentagonal pyramid, five within the same icosahedron, the sixth to an adjacent icosahedron or to an atom in 2b. The resulting framework is continuous in three dimensions. Typical intra- and intericosahedral bond distances are, respectively, 1.805 i.0.015 and 1.68i 0.03 A. Available single crystals of tetragonal boron are subject t o a large and variable degree of internal disorder: the diffraction data afforded by different specimens are notably diverse as regards strength of diffuse sc%ttering,distribution of Bragg intensities, and lattice constants. Typical values of lattice constants are a = 8.75, c = 5.06 A.
Introduction We have in progress intensive studies aimed a t a For many years only microcrystalline and often determination of structure for this form. The quite impure preparations of elemental boron were tetragonal6 modification of boron has been most available, yielding X-ray powder diffraction pat- studied.6 The present paper reports the detailed terns of notable complexity and diversity. Recent structural investigation of the tetragonal single single crystal studies of three different niodifica- crystals (appearing in two widely dissimilar growth tions show boron exhibiting a remarkably wide habits) prepared by Laubengayer, et a1.,6 through range of structural complexity. The most recently reduction of boron tribromide with hydrogen on a discovered and structurally simplest modification2 hot filament; the fundamental atomic arrangement. is rhombohedral with but one icosahedral Blz group within the fifty-atom cell of the earlier brief report& within the unit cell. The structural arrangement2 is ~ o n f i r m e d . ~ is intimately related to that of boron ~ a r b i d e , ~ (5) J. L. Hoard, S. Geller and R. E. Hughes, ibid., 73, 1892 B&,. The most easily prepared but structurally (1961). by far the most complex modification of boron also (6) A. W . Laubengayer, D . T. Hurd, A . E . Newkirk and J. L. is rhombohedralIQwith 108 atoms in the unit cell. Hoard, i b i d . , 66, 1924 (1943). (1) Supported by the Atomic Energy Commission under Contract No. AT(30-1)-878 and by the Research Corporation through a grant for purchase of major equipment used in this study. (2) L. V. McCarty. J . S. Kasper, F. N.Horn, B. F. Decker and A. E. Newkirk, THIS J O U R N A L , 80, 2592 (1958). (3) H. K. Clark and 1. L. Hoard, i b i d . , 66, 2115 (1943); G. S. Zhdanov and N. G. Sevast'yanov, Compl. rend. acad. scz '1 R S.S., 32, 432 (1941). (4) D. E. Sands and J. L. Hoard, THIS J O U R N A L , 79, 555'7 (1957).
(7) Based on the free use of authoritative single crystal data, we expect to prepare (or persuade others2 to prepare) for publication definitive tables for identifying the known modifications from X-ray powder data. We note here that the powder diff action patterns for "needle crystals" includes lines not characteristic of tetragonal boron. In taking "clusters" of needles for powdering a good deal of the microcrystalline matrix (formed a t a higher temperature since it directly ensheathed the filament) must have been included. The microcrystalline sheath formed in a run with a $lament temperature of ahout 1350' gave a powder pattern now identifiable' as t h a t of complex
4508
J. I,. HOARD, K. E. HUGHES AND D. E. SANDS
Crystallography of Tetragonal Boron.-Crystals of two distinct habits were found in the preparation6 of tetragonal boron. Most conimon were needles growing out from the heated filament more or less along the thermal gradient. The larger specimens, about 0.25 mni. in diameter, gave multiple diffraction spots; less imperfect smaller specimens about 0.10 mm. thick were found to be most useful. All needles showed the full diffraction symmetry of D41-,-4/mmm with the unique axis parallel to the needle axis. Twinning on (130) was invariably observed, the individual members being virtually equal in volume. The particularly small rods mentioned6 as rarely observed gave (weak) diffraction patterns which showed them to be early (but twinned) versions of the needles. Specimen needles large enough to give a useful range of diffraction intensities tended to be carrot-shaped with the blunt end away from the filament. It would appear that a t the low temperature (relative to the melting point) of deposition, boron from the vapor phase was deposited on the nearest available sites with little subsequent rearrangement. The second less commonly represented habit in the preparation6 was that of plates less than 0.05 mm. thick, virtually regular hexagons in outline, with an effective diameter up to about 0.3 mm. The plates generally were attached to the filament along an edge with the plate face approximately parallel to the thermal gradient. Despite all appearances to the contrary, the plates were shown to have the same fundamental structure as the needles, although lacking the invariable twinning of the latter. The following considerations may account in part for the simultaneous growth of crystals having such widely different habits. The axial ratio a/c of the tetragonal cell is almost precisely fi with c, the shortest and structurally simplest rational translation, as the probable direction of most rapid growth in a homogeneous environment. Formation of a nucleus with c even roughly along the high thermal gradient should result in a crystal of exaggerated needle-like habit. Formation of a nucleus with I: parallel to the filament surface and a secondary axis, say a2 along the thermal gradient might encourage growth in the latter direction comparable with that along c, giving dse to a crystal plate-like on (100). If, in addition, lateral faces f(OlO), i= (011)' (011) were about equally developed, the resulting crystal would appear as a hexagonal plate. The plate crystals had this aspect, although closer scrutiny indicated that eight extremely narrow faces of the form { 111 usually substituted in pairs for the four faces of { 011} cited above. One of the three face diagonals of the hexagon was along c; this unique direction was indicated by (easily overlooked) fine parallel striations present in the surface. Examination of several plates showed that the ragged edge of the hexagon, presumably indicating the line of attachment to the filament, was nearly parallel to the striations, ;.E., to c. On several specimens three consecutive angles of the rhombohedral boron. This result and the observed: transformation of the simplest modification suggest that the most complex structural form i s thermodynamically stable from the melting point downward t o about l ? O O o or perhaps lower.
Vol. 80
hexagon could be measured on thc microscope stage, each to better than one degree. Measured angles with were often found to depart from 120" by %--I", the sum of three consecutive angles not equal to 360" within the errors of measurement. The ideal crystallographic angles certainly were not preserved during rapid deposition in the high thermal gradient. Anomalous optical properties6 must surely be anticipated for very hard crystals grown in such an environment. Experimental The structural conclusions of this paper are based upo~r spectrometrically measured intensity data afforded b y two specimens selected from among about twenty examined by X-ray methods. h number of complicating features arising from various unsatisfactory characreristics of the boron crystals are summarized at this point. I n addition t o the invariable twinning on (130) of every needle, all speciri~enswere split into a t least two macroscopic components, albeit the departlire from parallel alignment in favorable cases corresponded t o less than tell rninutes of angular rotation. On Weissenberg or rut ation photographs, nevertheless, the doublet or multiplet char-ncter of the specimeil was rather conimonly obscured by lieavy diffuse scattering concentrated in the imniediatr vicinity of thc Bragg direction; by setting the crystal a t the liragg angle so as to limit the angular range for diffuse scattering (most conveniently on the spectrogoniometer with photographic recording) resolution of the macroscopic structure of the specimen and, in the appropriate sin O/A range, of the KO doublet of the radiation became apparent. T h e intensity of the diffuse scattering varied a good deal from one crystal to atlother, being a minimurn for the needle (111) chosen for spectrometric measurements, and substantially stronger for the selected plarc. Both needle :ind plate were macroscopic doubletons. Accompanying the variations in diffuse scattering as bet\veen specimens were measurable differences in lattice translations arid in the general distribution of Bragg intensities. Thus for Needle I (used in the original photographic work6 and for preliminary spectrometric measurements), we obtained a = 8.733 & 0.015, c = 5.030 & 0.003 A.; for Seetile I11 (chosen as best for spectronietrk measurements), a = 8.740 =t0.015,c = 5.068 & 0.010 A.; for Xeedle IV (shoving the largest value of c), c = 5.090 i:0.003 and for the-specimen plate, a = 8.771 & 0.013, c = 5.088 (1.015 A . Comparing Necdles I and IV, a minimum difference in c of 175 is established. The existence of variations in c.,though probable, is not certainly established. For fiftys atoms within the cell the calculated density of needle I11 is 2.33 g./cc. and of the plate, 2.29 g,/cc. The density of one of the needles as determined by flotation was reported8 as 2.31 g./cc. Photographic intensity data obtained by Dr. S. Geller for all reflections lying within the limiting sphere defined by the Cu K a wave-lenggths were used to determine the approximate structure o f tetragonal boron. It was clear that many reflections a t still higher sin e/?. must have large structure factors (the intensity distributionasQ was somewhat hypercentric for general reflections and completely so for the hkO and hhl data), but photographic recording with Mo Kcr radiation was not practicable for the available undersized specimens. The optimum thickness of sample for boron, taken as the reciprocal of the linear absorption COefficient, is about 1.6 mm. with Cu I ' 2 ; 4c: 0 '/2 0,1 1 2 0 0, 0 '/z 1/2, '/z 0 1,/2; cupancy of 2a or 4g. The following additional Fourier syntheses of am4 , l / 2 0 ',/4, 0 ' 1 2 3/4, '/z 0 3//4; and (the 4;: 0 icosahedron centers) 4e. Evidence Will be pre- plitude data for the plate were used in the evaluasented to show that there is partial filling of such tion of atomic parameters : p ( y , z ) , showing excelholes with extra boron atoms but in variable con- lent resolution of Bz and Bg; p(x,x,z), reproduced in centrations as between specimens. The holes 2a Fig. 3, showing complete resolution of B3, B4, Bb; are so large as to suggest the alternative use of po- the projected section p(y,z) for x = 0 + l / 4 , giving data on every variable parameter save one; line sitions 4g. 0 O z: O O Z: l / 2 j l / 2 , Z; I / z , ' 1 2 , 2 - z , with z 0.183. 4d appears to offer a syntheses of hkl data through B1 and B2 parallel to structurally less satisfactory, unused alternative to c to give z-coordinates of these atoms. Despite the erratic background (cf. Fig. 3 ) , the agreement in 4c. Occupation of icosahedral centers seems pos4ble only if there are neighboring framework va- parameter values among the several syntheses was rather good. The coordinates adopted as best cancies .2 Fourier synthesis, p ( x , y ) of hkO amplitudes representing the Fourier data for the plate were, for (Fig. 2 ) shows remarkably good resolution with no each structural class of atom, essentially those given overlapping between icosahedra, A quasi-fivefold by syntheses showing complete resolution for atoms
f 1. p\ii,%) is thus seen to furnish mutually perpcnd;cihr vicn-s of the asymmetric unit. Taking the u and v Coordinates as known from the earlier analysis, two quas i-independent values of Z for each structurtl class were read from p ( u , Z ) Difference syntheses, using a common Deb ye parameter for all atoms, were carried through three cycles of refinement with the following results: Indicated corrections along '4 were small, and none were introduced into the computation cycle. Convergence to a common value of the two determinations of Z was satisfactory for B4. The unresolved single peak was assigned minor weight in the refincment of 23,which oscillated about but returned to within 0.0005 of the Fourier value. From the outset the qumi-independent corrections to the Z-coordinate of B? were in opposite directions; even though the mean coordinate oscillated within a restricted range (
